设m是整数且k=4m+2,若f(sinx)=sinkx,求证f(cosx)=sinkx
问题描述：
设m是整数且k=4m+2,若f(sinx)=sinkx,求证f(cosx)=sinkx
答
ƒ(sinx) = sin(kx)
ƒ(cosx)
= ƒ[sin(π/2 - x)]
= sin[k(π/2 - x)]
= sin(kπ/2 - kx)
= sin[(4m + 2) • π/2 - kx]
= sin(2mπ + π - kx),m,k∈Z
= sin(π - kx)
= sin(kx)